Abstract <p>In fields such as robotics and wearable exoskeletons, the application of flexible shafts is gradually increasing, and they are being integrated into closed-loop control systems. As a result, the torsional stiffness of flexible shafts has become a critical parameter. Flexible shafts are composed of multiple layers of wound wires. During torsion, the wires experience both tensile deformation and compressive deformation between layers, making modeling and analysis complex. This paper proposes an algorithm for calculating the torsional stiffness of wire-wound flexible shafts. Hertz contact theory is employed to model and analyze the compressive deformation between layers, while the deformation theory of elastic curved rods is used to model and analyze the deformation of wires under force. By establishing boundary conditions, the compressive deformation and curved rod deformation are combined to calculate the torsional stiffness of the flexible shaft. The stiffness of two flexible shafts with different structures was calculated and experimentally tested. The results demonstrate that the proposed algorithm can accurately calculate the stiffness of flexible shafts in linear configurations.</p> Graphic abstract <p></p>